Interpreting Plots of a Multidimensional Dose-Response Surface in a Parallel Coordinate System

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Abstract
The dose-response surface for a combination of drugs is a multidimensional figure. Consequently, it is not possible to view such a surface using orthogonal axes when the number of dimensions exceeds 3. Parallel axes have been used to represent hyperdimensional figures. This paper reports on the use of parallel coordinate axes to plot the dose-response surface and its contour of constant response (isobols) for a combination of drugs. It is shown that pattern formed by intersecting line segments in the parallel system can aid in the interpretation of the fitted dose-response surface. More generally, analytic results are developed that permit the ready visualization and characterization of interaction effects of a polynomial model.